Gutter metal calculation

Gutters have the shape of a half-cylinder. Their diameter is 20 cm, and the total length around the roof is 35 m. How much is sheet metal needed to make them? Add 15% to the connections.

Final Answer:

A =  12.6449 m²

Step-by-step explanation:

$$\begin{gathered} D=20\text{cm}\to \text{m}=20:100\text{m}=0.2\text{m} \\ r=D/2=0.2/2=\frac{1}{10}=0.1\text{m} \\ l=35\text{m} \\ {S}_1=\pi \cdot r\cdot l=3.1416\cdot 0.1\cdot 35\doteq 10.9956{\text{m}}^2 \\ q=100\%+15\%=1+\frac{15}{100}=1.15 \\ A=S_1\cdot q=10.9956\cdot 1.15=12.6449{\text{m}}^2 \end{gathered}$$

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